Related papers: Identifiable learning of dissipative dynamics
The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…
Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external…
We present a variational autoencoder framework for learning and generating configurations of structured polymer globules from distance matrices. We used coarse-grained molecular dynamics to sample polyethylene structures, which we used as…
We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state…
Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now,…
We propose a new architecture for the learning of predictive spatio-temporal motion models from data alone. Our approach, dubbed the Dropout Autoencoder LSTM, is capable of synthesizing natural looking motion sequences over long time…
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements, without requiring access to velocity data. This is particularly relevant in system identification tasks where…
Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…
Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general $\mathbf{L}^2$ initial data in two space dimensions and…
We present a new method for learning control law that stabilizes an unknown nonlinear dynamical system at an equilibrium point. We formulate a system identification task in a self-supervised learning setting that jointly learns a controller…
We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…